Shadow Reduction in Ultrasound Imaging Using Differentiable Simulation and Radiance Field Decomposition

Background

• Ultrasound’s portability, low cost, and low risk make it suitable for repeated prenatal examinations, despite low signal-to-noise ratio and physics-based artefacts that obscure relevant structures..Source: §1 · p. 2

Motivation

• Skull attenuation often makes the proximal fetal brain hemisphere less visible than the distal hemisphere, limiting bilateral symmetry assessment, an important neurodevelopmental biomarker.Improving proximal-hemisphere visibility could increase usable image information.Source: §1 · p. 2

Limitations of prior methods

• Existing shadow-reduction methods rely on restrictive tissue assumptions, require unavailable RF frequency data, or risk hallucinated anatomy and poor generalization across probes.Conventional pipelines can also under- or over-expose regions when heterogeneous tissue violates assumptions of similar energy reduction across scanlines.Source: §1 · pp. 2–3

RFlash

• RFlash decomposes ultrasound images into physically interpretable parameter maps using differentiable simulation, then renders attenuation-corrected images as if the transducer had advanced through tissue.This reduces the dependence of each rendered depth on proximal tissue, preventing proximal structures from casting shadows onto deeper regions.Source: §1 · p. 3
• RFlash’s canonical scanline-based post-processing supports linear and curvilinear probes and both 2D and 3D ultrasound without hardware constraints..Source: §1 · p. 4

Evaluation overview

• Across fetal brain, real abdominal, and simulated liver data, RFlash improves image quality and reduces shadow-related intensity differences; recovered proximal-hemisphere information also benefits fetal age prediction.Attenuation-derived shadow-confidence maps are informative for random-forest shadow segmentation and perform well against existing methods.Source: §1 · p. 4

2.1. Shadow Artefact Reduction and Detection

• Earlier B-mode shadow-reduction methods use statistical or closed-form estimates; Knipp et al. and Hughes and Duck assume linear attenuation–scattering relations, while frequency-shift methods require RF data.The authors identify Hughes and Duck as their baseline because it operates as post-processing on B-mode images without annotation for training or inference.Source: §2.1 · p. 4
• GAN-based approaches can produce plausible results but risk hallucinating anatomy; RFlash instead processes B-mode images without RF data or complex per-iteration solvers and trains per image, reducing knowledge transfer and hallucination risk.Earlier methods also include iterative optimization, such as Yu and Wang’s per-iteration partial differential equation [18].Source: §2.1 · pp. 4, 6

2.2. Radiance Fields

• Prior radiance fields reconstruct 3D ultrasound volumes from 2D slices; RFlash is, to the authors’ knowledge, the first to apply them to ultrasound shadow reduction, modeling tissue physics rather than appearance.It uses cross-sectional slice data, treats each ray as a direct observation of local acoustic interactions, and adopts an explicit representation for fast training and transparent parameter estimates.Source: §2.2 · p. 6

2.3. Ultrasound Simulation

• Convolutional and point-spread-function simulators approximate scatterer interference but do not explicitly model scanline shadows, while more realistic extensions can be costly or non-differentiable.RFlash uses a simplified differentiable ray model that ignores cross-scattering, models intensities directly, and avoids point-spread-function convolution for fast, physically consistent iterative optimization and shadow correction.Source: §2.3 · pp. 6–7

3.1. Ultrasound image formation model

• Beamformed inputs are modeled as independent scanlines with TGC, envelope detection, log compression, and scan conversion; A/D conversion and binning are excluded.For 3D data, the scanline–depth coordinates are mapped to Cartesian volumes, with probe geometry taken into account.Source: §3.1 · pp. 7–8, Figure 4 · p. 9

3.2. Explicit radiance-field representation

• RFlash represents attenuation and scatter intensity in explicit volumetric maps, sampled by trilinear interpolation and optimized against rendered reference images rather than with an MLP.The explicit representation is straightforward to initialize, inspect, and optimize, but uses more memory.Source: §3.2 · pp. 8–10

3.3. Differentiable ultrasound simulation

• Attenuation A and scatter intensity Φ parameterize local signal loss and backscatter; the forward simulator applies pathwise exponential attenuation, depth-dependent TGC, and log compression to produce B-mode images.The model assumes constant sound speed and does not separately estimate reflection or refraction.Source: §3.3 · pp. 10–11

3.4. Shadow-reduced rendering

• After fitting tissue maps with the realistic forward operator, RFlash adaptively compensates for spatially varying attenuation and re-renders scatter intensity without attenuation to reduce shadows.This compensation cancels the attenuation term in the forward model.Source: §3.1 · p. 8, §3.4 · p. 11

3.5. Shadow confidence maps

• The shadow-confidence map compares measured and shadow-reduced images in the linear intensity domain, then normalizes the attenuation-related intensity ratio.The comparison uses the log-compression operator to return to linear intensity.Source: §3.5 · p. 12

4.1. Datasets

• Evaluation covered 1,261 3D fetal-head volumes, 143 usable real abdominal scans from a 213-scan set [49], and 1,200 simulated linear-probe liver scans.The shadow-map evaluation also used 14 2D curvilinear fetal scans with determinable geometry; these were excluded from general method evaluation because their statistical power was too small.Source: §4.1 · p. 13, §4.4 · p. 15

4.2. Baseline shadow reduction

• The Hughes and Duck post-processing baseline adapts their RF-data method by assuming scattering intensity and attenuation are linearly dependent; its output is termed Hughes shadow reduction.The study describes undoing log compression to apply the reformulated method to sampled image slices.Source: §4.2 · pp. 13–14

4.3. Implementation details

• Training used weighted SSIM and L2 losses, Adam at a 0.03 learning rate for 300 epochs, and took under one minute per 3D fetal volume on an RTX 4090.Parameter maps were initialised at A = 1.2 and Φ = 4.25; input normalization used mean 4.25 and standard deviation about 1.4167, and g = 80.Source: §4.3 · p. 14

4.4. Evaluation: Measurement of shadows

• Shadow impact was measured as the difference between mean grey values in shadowed and non-shadowed regions after histogram equalization, averaged over the whole image.Positive values indicate higher mean intensity in non-shadowed regions; evaluations used all available datasets except the 14-scan shadow-map set [50].Source: §4.4 · pp. 14–15

4.5. Evaluation: Age prediction as clinical downstream task

• A 3D ResNet-10 trained on the distal hemisphere of 1,261 fetal volumes was tested on both hemispheres to assess generalization to the proximal hemisphere.The subject-level train, validation, and test split was 868, 133, and 260, respectively; volumes were aligned to common space and size-normalized.Source: §4.5 · p. 15

4.6. Evaluation: Consistency of shadow maps

• Shadow-map consistency was assessed visually and through random-forest bone-shadow segmentation, comparing image-only inputs with inputs augmented by Ultra-NeRF or RFlash confidence maps.The setup followed the evaluation model and datasets of Yesilkaynak et al. and examined numerical performance and feature importance.Source: §4.6 · pp. 15–16

5.1. Numerical Results

• Across 3D fetal-brain, curvilinear abdominal, and linear liver images, RFlash reduced shadows; it revealed the proximal Sylvian fissure and avoided Hughes’s over-brightening and enhancement artefacts.Fetal-brain structures became more visible where sufficient image information was available for reconstruction.Source: §5 · p. 16, Figure 7 · p. 17
• RFlash significantly outperformed Hughes on all real datasets, while Hughes had the best numerical score on simulated images despite RFlash’s stronger visual results there.The numerical metric did not capture enhancement artefacts.Source: §5.1 · p. 16, Figure 7 · p. 17, Table 1 · p. 18

5.2. Age Prediction as Clinical Downstream Task

• RFlash reduced proximal-hemisphere age-prediction error by approximately 5 days (40%) versus original images and almost 2 days (19%) versus Hughes.Prediction accuracy improved for both hemispheres, including the distal hemisphere used for training; the largest benefit was proximal.Source: §5.2 · p. 18, Table 2 · p. 18
• RFlash improved predictability in both hemispheres, with a stronger effect proximally, although distal hemispheres remained more predictive on average.Individual samples showed considerable spread, reflecting differences in image quality.Source: §5.2 · pp. 18–19, Figure 8 · p. 19

5.3. Shadow Confidence Maps

• Random forests using RFlash shadow maps performed better than Wysocki et al. maps on all metrics except precision, and produced visually more physically plausible shadow segmentations.Predictions remained imperfect but segmented shadows through the lower edge of the frame.Source: §5.3 · p. 20, Table 3 · p. 21, Figure 11 · p. 22
• SHAP analysis indicated that RFlash confidence maps were more informative to the random forest than Yesilkaynak et al. maps.The forest relied more on the RFlash confidence map than on the baseline map.Source: §5.3 · p. 20, Figure 12 · p. 23

Discussion

• RFlash explicitly decomposes images into physics-informed attenuation and scatter-intensity maps, then re-renders them to reduce each depth’s dependence on intervening tissue.The approach uses a differentiable ultrasound simulator and an explicit radiance-field representation; re-rendering can be interpreted as virtually moving the probe through tissue.Source: §6 · p. 23
• As post-processing, RFlash avoids vendor-specific scanner access and supports different 2D and 3D ultrasound geometries; individual-image training entails no cross-patient knowledge transfer.Evaluation across probe geometries and acquisition types supports robustness to variation in input ultrasound data.Source: §6 · p. 24
• On real data, RFlash outperformed the Hughes shadow-reduction baseline in the proposed shadow metric and improved proximal-hemisphere age prediction over both original images and the baseline.RFlash also produced more uniform contrast and increased visibility of structures in the shadow-affected proximal hemisphere.Source: §6 · p. 24
• RFlash’s attenuation-derived shadow-confidence maps provided stronger guidance for random-forest shadow segmentation than Wysocki et al.’s maps, and received greater SHAP importance.The maps are computed directly from the attenuation-related decomposition, providing an interpretable estimate of shadow formation.Source: §6 · p. 24
• RFlash cannot recover structures absent from the input, requires accurate geometry estimates, and runs slower than closed-form methods.Geometry estimation was non-trivial for the abdominal dataset; the code is unoptimized, and hardware-optimized implementation may shorten runtime.Source: §6 · pp. 24–25

• The authors declare no known competing financial interests or personal relationships that could have influenced the work.Source: Declaration of Interests · p. 25
• A priority application for the method has been filed at the UK Intellectual Property Office.Source: Declaration of Interests · p. 25

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process.

• The authors used GitHub Copilot and OpenAI’s Codex for code snippets, figures, and writing support, but not to generate the work’s ideas, results, or structure.They reviewed and edited the content as needed and take full responsibility for the published article.Source: Declaration of generative AI and… · p. 25

Appendix A.1. Additional Numerical Results

• Table A.4 evaluates mean intensity difference across datasets using RFlash shadow maps, reporting means ± standard deviations and subject-wise differences relative to RFlash.The caption marks differences significantly different from 0 by t-test at p<0.01; adjacent text gives 0.001667 for multiple-comparison correction.Source: Table A.4 · p. 34, Appendix A.1 · p. 34
• Table A.5 evaluates mean intensity difference across datasets using Hughes shadow maps, reporting means ± standard deviations and subject-wise differences relative to RFlash.The caption marks differences significantly different from 0 by t-test at p<0.01; adjacent text gives 0.001667 for multiple-comparison correction.Source: Table A.5 · p. 34, Appendix A.1 · p. 34

Appendix A.2. Additional Results Age Prediction

• Figure A.13 complements Figure 8 by showing the individual data points underlying the convex hulls in that figure.Source: Figure A.13 · p. 35

Appendix B.1. Sensitivity with respect to sampling in simulation space

• Figure B.14 plots similarity measures between simulated and original volumes against sampling-cube edge length n, marking the chosen value.The edge length is measured in simulation space.Source: Figure B.14 · p. 35
• Figure B.15 shows example volumes reconstructed using different simulation-space sampling densities.Source: Figure B.15 · p. 36

Appendix B.2. Sensitivity to initial values

• Figure B.16 presents shadow-reduction heat maps for different initial-value combinations and marks the selected combination.Source: Figure B.16 · p. 37

Appendix B.3. Sensitivity with respect to loss function weighting

• Figure B.17 plots converged SSIM and L2 values across loss-function weighting factors, marking the chosen value.Source: Figure B.17 · p. 38

Appendix B.4. Convergence behaviour

• Figure B.18 plots L2 and SSIM over epochs to show convergence behaviour and marks the chosen value.Source: Figure B.18 · p. 38

Appendix B.5. Sensitivity of the shadow metric to the number of histogram buckets

• Figure B.19 plots the means and confidence intervals of three metrics across histogram-bucket counts, marking the chosen value in red.Source: Figure B.19 · p. 39